Computing Maximal Stability Region Using a Given Lyapunov Function

In this paper, we are interested in computing a nonlinear system´s maximal stability domain using a given Lyapunov function. This problem is formulated as computing the smallest positive zero of a Lipschitz continuous function. Using the continuity property of the local maximizers of this function, we propose an algorithm to compute such a zero. The effectiveness of the proposed algorithm is demonstrated by an example.